Jesus turns the tables on his detractors. He asks them a thorny scriptural question that contradicts their common wisdom and opens the door for them to recognize his authority if they're willing. But sadly, they are not. So Jesus speaks an open warning that his disciples, the crowds, and even the Jewish leaders can hear: Beware of them, beware of their love of appearances, of their longing for human recognition. They love status. They serve themselves rather than living in submission and dependence on God. Jesus says they "devour widows' houses" -- a ringing condemnation that echoes many of the prophets. (I'm currently reading Amos, and his condemnation of the Israelites' social injustice and their religious hypocrisy and showmanship are lockstep with Jesus at this point.)
Then Jesus moves on to contrast an actual widow with these leaders. Remember that the chapter divisions were added later. If you were just reading through this text as a narrative, it would be hard to miss the obvious connection between "widows' houses" and the widow who, out of her poverty and out of her faith offers her pittance to God. She becomes the poster child for trust and submission, in contrast to the scribes' scheming and self-focus. She is living out Jesus' command in the Sermon on the Mount (Matthew 5-7) to "seek first God's kingdom and his righteousness" and to lay up treasures in heaven. Jesus makes this connection explicit when he comments on her giving by saying "this poor widow has put in more than all of them."
As we'll see next time, the self-seeking power games of the scribes and authorities bring down not only condemnation on themselves, but on the whole temple institution and the future of Israel as a political entity. Again, Jesus echoes the prophets when he says that their agendas and refusal to recognize what God is doing will not stand.